The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.
For maximum r, r'(x) = 0
It becomes: r'(x) =
=
x= 200
Hence, r(200) =
Solving it we get,
r(200) = 1000
Hence, maximum revenue is $1000.
K is the midpoint, so and
, and along with the congruent vertical angles (
and
), you would use the SAS (side angle side) congruence theorem to prove the inner pairs of triangles to be congruent.
So, (top and bottom triangles) and
(left and right triangles).
Then through CPCTC, we can show the corresponding pieces are congruent leading to and
showing the opposite sides of the quadrilateral are congruent. Therefore we do have a parallelogram and enough information to prove it as such.
Side note: CPCTC stands for "corresponding parts of congruent triangles are congruent".
Given:
Principal value = $8,008
Rate of interest = 2% compounded 6 times per year.
Time = 16 years
To find:
The account balance after 16 years.
Solution:
The formula for amount is:
Where, P is principal, r is the rate of interest, n is the number of times interest compounded in an year and t is the number of years.
Putting in the above formula, we get
Therefore, the account balance after 16 years is $11022.17.